David Cameron will seek to prevent Ed Miliband's "one nation" Labour driving him from the common ground of British politics on Wednesday, asserting that his brand of compassionate Conservatism is not just for the strong, but also the best way to help the poor, the weak and the vulnerable.

Despite a conference full of tough messages on burglary, welfare and sometimes social issues, the prime minister will insist: "My mission from the day I became leader was … to show the Conservative party is for everyone, north or south, black or white, straight or gay."

In his annual speech to the Conservative party conference, he will tell his party: "It's not enough to know our ideas are right. We've got to explain why they are compassionate too."

His aides decline to refer to the political "centre ground" arguing that on issues such as welfare, crime and Europe, the common ground is to the right, and in territory long occupied by the Conservatives. He will also refuse to bury the much derided "big society" concept in his keynote speech closing the conference season saying his task is "above all to show Conservative methods are not just the way we grow a strong economy, but the way we build a big society".

But on the day after the IMF issued another downgrade of its UK growth forecasts, Cameron will also issue a stark, almost existential, warning to the country, saying unparalleled global forces mean the country is at an hour of reckoning.

He will say: "Unless we act, unless we take difficult decisions, unless we show determination and imagination, Britain may not be the force which it has been in the past. The truth is this we are in a global race today and that means an hour of reckoning for a country like ours – sink or swim, do or die."

At the same time, flashes of his trademark optimism will appear, drawing on the revival of the British spirit shown in the Olympic summer.

Cameron's aides believe that Miliband's largely insular address to his own party totally failed to address not just the deficit but the scale of competitive challenge facing Britain due to rise of new global powers. He will argue that these forces require tough decisions on spending, welfare, and schools if the strivers working hard are not to feel cheated.

The prime minister's aides acknowledge that although Miliband, in personal terms, delivered a strong speech, they estimate he has made two major strategic errors in failing to make tough decisions on the deficit or show a greater willingness to curb the welfare budget.

Cameron will say: "Labour's plans to borrow more is actually a massive gamble with our economy and with our future. We're here because they spent too much money and borrowed too much. How can the answer be more spending and more borrowing. I honestly think Labour has not learned a thing."

George Osborne upped the stakes by claiming a fundamental threat to the free enterprise system now existed, adding to claims made by Cameron that Labour is waging class war.

He told a meeting of businessmen in Birmingham: "Really for the first time in my adult lifetime, up for grabs is the argument about a free enterprise economy.

"That was really resolved I thought at the end of my teenage years when the Berlin Wall fell and all parties and all groups in Britain basically accepted the consensus of the free market economy.

"I would say you just see signs of that being contested, contested because of what's happened in the banking crash, and people are starting to say it's OK for the state to take 50% of the national income, it's OK for the state to tax people 50% of their income, it's actually wrong to challenge vested interests in our education and welfare system."

In an implicit acknowledgement that the electorate remains confused about his core values, Cameron will reveal more than he has ever done before about his personal background.

Cameron will not present himself as a hard luck story, but the son of a man that suffered disability, stigma, loneliness and a broken family. Cameron's father Ian died two years ago aged 77 and had been born with both legs deformed, and endured repeated operations in an attempt to straighten them. "Because disability in the thirties was such a stigma, he was an only child and probably a lonely child," Cameron will say.

Challenging those who see the Conservatives as the party of snobs and the rich, he will say: "There is nothing complicated about me. I believe in working hard, caring for my family and serving my country".

Cameron found himself under growing pressure over his plans to cut the welfare budget, with Liberal Democrat grassroots bodies demanding that Nick Clegg does not sign up to such measures. They are furious that their plan to raise taxes through a "mansion tax" has been thrown out by the chancellor. There is suspicion in Lib Dem circles that Clegg has in broad terms agreed to this level of welfare cuts, something his officials hotly deny.

Mark Garnier, a member of the Treasury select committee, said at a fringe event: "The reason we have a low interest rate is because the economy is absolutely screwed." But Cameron rejected a change: "It's not Plan B that we need, what we are doing is making sure that every part of Plan A is firing on all cylinders."